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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (21 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1694.4.a.a	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$-10$	$-14$	$-7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-10q^{3}+4q^{4}-14q^{5}+20q^{6}+\cdots$
1694.4.a.b	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$-12$	$-7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}-12q^{5}+4q^{6}+\cdots$
1694.4.a.c	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$18$	$-7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}+18q^{5}+4q^{6}+\cdots$
1694.4.a.d	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$7$	$3$	$-7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+7q^{3}+4q^{4}+3q^{5}-14q^{6}+\cdots$
1694.4.a.e	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$2$	$-5$	$-1$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-5q^{3}+4q^{4}-q^{5}-10q^{6}+\cdots$
1694.4.a.f	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$2$	$0$	$2$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+2q^{5}+7q^{7}+8q^{8}+\cdots$
1694.4.a.g	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$2$	$8$	$-14$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+8q^{3}+4q^{4}-14q^{5}+2^{4}q^{6}+\cdots$
1694.4.a.i	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{133}) $	None	✓	$1$	$1$	$-4$	$-5$	$-2$	$-14$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-\beta )q^{3}+4q^{4}-q^{5}+\cdots$
1694.4.a.m	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{133}) $	None	✓	$1$	$1$	$4$	$-5$	$-2$	$14$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2-\beta )q^{3}+4q^{4}-q^{5}+\cdots$
1694.4.a.n	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$4$	$-4$	$-13$	$14$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-6\beta )q^{3}+4q^{4}+(-12+\cdots)q^{5}+\cdots$
1694.4.a.o	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$4$	$6$	$2$	$14$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(2+2\beta )q^{3}+4q^{4}+(6-10\beta )q^{5}+\cdots$
1694.4.a.q	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.27093.1	None	✓	$1$	$1$	$-6$	$-5$	$-5$	$-21$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1694.4.a.r	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.46700.1	None	✓	$1$	$1$	$-6$	$-5$	$5$	$21$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1694.4.a.t	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.27093.1	None	✓	$1$	$1$	$6$	$-5$	$-5$	$21$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1694.4.a.u	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.46700.1	None	✓	$1$	$1$	$6$	$-5$	$5$	$-21$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1694.4.a.x	$1694$	$4$	1694.a	1.a	$1$	$4$	$4$	$99.949$	4.4.4388525.1	None	✓	$1$	$1$	$8$	$-10$	$2$	$28$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+3\beta _{2})q^{3}+4q^{4}+(2+\cdots)q^{5}+\cdots$
1694.4.a.bd	$1694$	$4$	1694.a	1.a	$1$	$6$	$6$	$99.949$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$-12$	$-10$	$-8$	$42$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1694.4.a.be	$1694$	$4$	1694.a	1.a	$1$	$6$	$6$	$99.949$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$12$	$-10$	$-8$	$-42$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1694.4.a.bf	$1694$	$4$	1694.a	1.a	$1$	$8$	$8$	$99.949$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-16$	$12$	$-7$	$56$	$+$	$-$	$+$	$-$	$11$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{2})q^{3}+4q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
1694.4.a.bj	$1694$	$4$	1694.a	1.a	$1$	$10$	$10$	$99.949$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-20$	$17$	$11$	$-70$	$+$	$+$	$-$	$-$	$3^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots$
1694.4.a.bk	$1694$	$4$	1694.a	1.a	$1$	$10$	$10$	$99.949$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$20$	$-3$	$-27$	$-70$	$-$	$+$	$+$	$-$	$11^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-3-\beta _{4}+\cdots)q^{5}+\cdots$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.